Image texture on extruded SVG
You don't really need to convert the curve to mesh. 


Import the SVG
Create a material
Use an image texture in the material
Select the image you want to use
Create an empty
Select your object again and in the materials set the coordinates to object
Select the empty as the control object for the coordinates.


If you switch to rendered view you should be able to see the texture being used as part of the material of the curve.



To control the placement and size of the image move/scale/rotate the empty.



For Blender internal is the exact same procedure: create a material, create a texture, set it to use object coordinates and use an empty to control them.